Ryan ASCII notation
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A system of using ASCII characters to notate any fractional frequency in Just Intonation. Created by the musician and theorist David Ryan * Preprint: http://arxiv.org/pdf/1508.07739 **Abstract:** Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve-note tuning systems the frequency can be described using letters A to G with sharp or flat symbols. For Just Intonation tuning systems these symbols are insufficient. This paper provides a system for describing any frequency which is a rational number multiplied by a suitable base frequency. Explicit notation is given for low prime numbers, and an algorithm for higher primes described. **Key features:** Can be inputted by computer keyboard alone (ASCII characters) Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied Simple notations exist for 3-limit, 5-limit, 7-limit JI notes Look-up table for providing ASCII notation for higher primes (11/8, 109/100, etc) Algorithm for deriving these notations Very compact notation for octave equivalence classes Good for describing all the notes on a 5-limit or 7-limit tone lattice **Challenges:** Octaves are not sequential - easier to understand octave equivalence classes than exact notes . ( Example: C = 1/1 F = 4/3 G = 3/4 but 3/2 = `G so 3/2 requires an octave modifier to describe.) **Notation examples:** //2-limit:// C = 1/1 `C = 2/1 (definition of octave modifier using ` character to prefix) ,C = 1/2 (definition of octave modifier using , character to prefix) ,,,C = 1/8 //3-limit:// F = 4/3 (definitions of the 7 note names here) C = 1/1 G = 3/4 D = 9/16 A = 27/64 E = 81/256 B = 243/1024 Bb = 16/9 (definition of a flat b character) F# = 729/4096 (definition of a sharp # character) C# = 2187/16384 (this is equivalent to a sharp # character) Cb = 16384/2187 (this is equivalent to a flat b character) `G = 3/2 ```D = 9/2 //5-limit:// E' = 5/4 (definition of ' modifier) Ab. = 4/5 (definition of . modifier) A' = 4/3 ``E' = 5/1 `B' = 15/8 //7-limit// Bb~7 = 7/8 (definition of ~7 modifier) D_7 = 8/7 (definition of _7 modifier) F~7 = 21/16 `Bb~7 = 7/4 `F~7 = 21/16 Eb~7 = 7/6 //Higher p-limits// F#~11 = 11/8 (definition of ~11 modifier) Gb_11 = 8/11 (definition of _11 modifier) ``F#~11 = 11/2 B~11 = 11/6 Ab~13 = 13/16 C#~17 = 17/16 Eb~19 = 19/16 F#~23 = 23/32 etc (separate definition for each prime) **Calculation examples** The golden rule in this notation is: to derive notation for a more complicated fraction, break it down into simpler fractions; fractions with notation already known. In particular, separate out the fractions for each higher prime. 55/32 = (11/8)*(5/4) = F#~11 * E' = A#'~11 7/5 = (7/8)*(4/5)*(2/1) = Bb~7 * Ab. * `C = `Bb.~7 * Ab = `Gb.~7 30/1 = (2/1)*(3/1)*(5/1) = (32/1)*(3/4)*(5/4) = `````C * G * E' = `````G' * E = `````B' (Notice how modifiers ` for octave and ' for prime 5 can be moved about freely) 19/13 = (19/16) * (16/13) = Eb~19 * (Ab~13)^-1 = Eb~19 * E_13 = G~19_13 **Other links** Some music created using this notation is available at: * Dave Ryan's SoundCloud page: https://soundcloud.com/daveryan23
Original HTML content:
<html><head><title>Ryan ASCII notation</title></head><body>A system of using ASCII characters to notate any fractional frequency in Just Intonation. Created by the musician and theorist David Ryan<br /> <br /> <ul><li>Preprint: <!-- ws:start:WikiTextUrlRule:88:http://arxiv.org/pdf/1508.07739 --><a class="wiki_link_ext" href="http://arxiv.org/pdf/1508.07739" rel="nofollow">http://arxiv.org/pdf/1508.07739</a><!-- ws:end:WikiTextUrlRule:88 --></li></ul><br /> <strong>Abstract:</strong><br /> Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve-note tuning systems the frequency can be described using letters A to G with sharp or flat symbols. For Just Intonation tuning systems these symbols are insufficient. This paper provides a system for describing any frequency which is a rational number multiplied by a suitable base frequency. Explicit notation is given for low prime numbers, and an algorithm for higher primes described.<br /> <br /> <strong>Key features:</strong><br /> Can be inputted by computer keyboard alone (ASCII characters)<br /> Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied<br /> Simple notations exist for 3-limit, 5-limit, 7-limit JI notes<br /> Look-up table for providing ASCII notation for higher primes (11/8, 109/100, etc)<br /> Algorithm for deriving these notations<br /> Very compact notation for octave equivalence classes<br /> Good for describing all the notes on a 5-limit or 7-limit tone lattice<br /> <br /> <strong>Challenges:</strong><br /> Octaves are not sequential - easier to understand octave equivalence classes than exact notes . ( Example: C = 1/1 F = 4/3 G = 3/4 but 3/2 = `G so 3/2 requires an octave modifier to describe.)<br /> <br /> <strong>Notation examples:</strong><br /> <br /> <em>2-limit:</em><br /> C = 1/1<br /> `C = 2/1 (definition of octave modifier using ` character to prefix)<br /> ,C = 1/2 (definition of octave modifier using , character to prefix)<br /> ,,,C = 1/8<br /> <br /> <em>3-limit:</em><br /> F = 4/3 (definitions of the 7 note names here)<br /> C = 1/1<br /> G = 3/4<br /> D = 9/16<br /> A = 27/64<br /> E = 81/256<br /> B = 243/1024<br /> Bb = 16/9 (definition of a flat b character)<br /> F# = 729/4096 (definition of a sharp # character)<br /> C# = 2187/16384 (this is equivalent to a sharp # character)<br /> Cb = 16384/2187 (this is equivalent to a flat b character)<br /> `G = 3/2<br /> ```D = 9/2<br /> <br /> <em>5-limit:</em><br /> E' = 5/4 (definition of ' modifier)<br /> Ab. = 4/5 (definition of . modifier)<br /> A' = 4/3<br /> ``E' = 5/1<br /> `B' = 15/8<br /> <br /> <em>7-limit</em><br /> Bb~7 = 7/8 (definition of ~7 modifier)<br /> D_7 = 8/7 (definition of _7 modifier)<br /> F~7 = 21/16<br /> `Bb~7 = 7/4<br /> `F~7 = 21/16<br /> Eb~7 = 7/6<br /> <br /> <em>Higher p-limits</em><br /> F#~11 = 11/8 (definition of ~11 modifier)<br /> Gb_11 = 8/11 (definition of _11 modifier)<br /> ``F#~11 = 11/2<br /> B~11 = 11/6<br /> Ab~13 = 13/16<br /> C#~17 = 17/16<br /> Eb~19 = 19/16<br /> F#~23 = 23/32<br /> etc (separate definition for each prime)<br /> <br /> <strong>Calculation examples</strong><br /> The golden rule in this notation is: to derive notation for a more complicated fraction, break it down into simpler fractions; fractions with notation already known. In particular, separate out the fractions for each higher prime.<br /> <br /> 55/32 = (11/8)*(5/4) = F#~11 * E' = A#'~11<br /> 7/5 = (7/8)*(4/5)*(2/1) = Bb~7 * Ab. * `C = `Bb.~7 * Ab = `Gb.~7<br /> 30/1 = (2/1)*(3/1)*(5/1) = (32/1)*(3/4)*(5/4) = <!-- ws:start:WikiTextRawRule:00:```` --><!-- ws:end:WikiTextRawRule:00 -->`C * G * E' = <!-- ws:start:WikiTextRawRule:01:```` --><!-- ws:end:WikiTextRawRule:01 -->`G' * E = <!-- ws:start:WikiTextRawRule:02:```` --><!-- ws:end:WikiTextRawRule:02 -->`B' (Notice how modifiers ` for octave and ' for prime 5 can be moved about freely)<br /> 19/13 = (19/16) * (16/13) = Eb~19 * (Ab~13)^-1 = Eb~19 * E_13 = G~19_13<br /> <br /> <strong>Other links</strong><br /> Some music created using this notation is available at:<br /> <ul><li>Dave Ryan's SoundCloud page: <!-- ws:start:WikiTextUrlRule:89:https://soundcloud.com/daveryan23 --><a class="wiki_link_ext" href="https://soundcloud.com/daveryan23" rel="nofollow">https://soundcloud.com/daveryan23</a><!-- ws:end:WikiTextUrlRule:89 --></li></ul></body></html>